This study is the first one looking at three new HIV vaccines in HIV-infected children to determine the safety of the three products and to evaluate what effect the vaccines will have on the underlying immune deficiency and on the activity of the virus itself. The study includes 80 children, half at lower doses and half at higher doses. One third will receive either vaccine or the adjuvant or alum placebo used with each vaccine. This study is not designed to compare the three vaccines.